30. In a typical tension test a dog-bone shaped specimen is pulled in a machine. During the test, the force F needed to pull the specimen and the length L of a gauge section are measured. This data is used for plotting a stress-strain diagram of the material. Two definitions, engineering and true, exist for stress and strain. The engineering stress o and strain Lo are L-Lo , where Lo and Ao are the initial gauge Lo defined by oe = and A0 をミ length and the initial cross-sectional area of the specimen, respectively. The FL = In To true stress o, and strain e are defined by o, and %3D Ao Lo The following are measurements of force and gauge length from a ten- sion test with an aluminum specimen. The specimen has a round cross sec- tion with a radius of 0.25 in. (before the test). The initial gauge length is 0.5 in. Use the data to calculate and generate the engineering and true stress- strain curves, both on the same plot. Label the axes and use a legend to identify the curves. Units: When the force is measured in pounds (lb) and the area is calculated in in.2, the unit of the stress is psi (pounds per square inch). F (lb) L (in.) 0. 4,390 7,250 10,780 11,710 12,520 12,800 13,340 0.50146 0.50226 0.50344 0.50423 0.50577 0.50693|0.51138 0.5 F (lb) L (in.) 0.52006 0.52169 0.52362 0.52614|0.53406 0.540180.56466| 13,740 13,820 13,850 | 13,910 13,990 || 14,020 | 14,130
30. In a typical tension test a dog-bone shaped specimen is pulled in a machine. During the test, the force F needed to pull the specimen and the length L of a gauge section are measured. This data is used for plotting a stress-strain diagram of the material. Two definitions, engineering and true, exist for stress and strain. The engineering stress o and strain Lo are L-Lo , where Lo and Ao are the initial gauge Lo defined by oe = and A0 をミ length and the initial cross-sectional area of the specimen, respectively. The FL = In To true stress o, and strain e are defined by o, and %3D Ao Lo The following are measurements of force and gauge length from a ten- sion test with an aluminum specimen. The specimen has a round cross sec- tion with a radius of 0.25 in. (before the test). The initial gauge length is 0.5 in. Use the data to calculate and generate the engineering and true stress- strain curves, both on the same plot. Label the axes and use a legend to identify the curves. Units: When the force is measured in pounds (lb) and the area is calculated in in.2, the unit of the stress is psi (pounds per square inch). F (lb) L (in.) 0. 4,390 7,250 10,780 11,710 12,520 12,800 13,340 0.50146 0.50226 0.50344 0.50423 0.50577 0.50693|0.51138 0.5 F (lb) L (in.) 0.52006 0.52169 0.52362 0.52614|0.53406 0.540180.56466| 13,740 13,820 13,850 | 13,910 13,990 || 14,020 | 14,130
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Question
Transcribed Image Text:30. In a typical tension test a dog-bone
shaped specimen is pulled in a
machine. During the test, the force F
needed to pull the specimen and the
length L of a gauge section are measured. This data is used for plotting a
stress-strain diagram of the material. Two definitions, engineering and true,
exist for stress and strain. The engineering stress
F
de
and strain
e are
defined by oe
F
%3D
and
A0
L-Lo where Lo and Ao are the initial gauge
6, =
Lo
length and the initial cross-sectional area of the specimen, respectively. The
true stress o, and strain e are defined by o,
는는 and q
%3D
= In
A0 Lo
The following are measurements of force and gauge length from a ten-
sion test with an aluminum specimen. The specimen has a round cross sec-
tion with a radius of 0.25 in. (before the test). The initial gauge length is 0.5
in. Use the data to calculate and generate the engineering and true stress-
strain curves, both on the same plot. Label the axes and use a legend to
identify the curves.
Units: When the force is measured in pounds (lb) and the area is calculated
in in.2, the unit of the stress is psi (pounds per square inch).
F (lb)
0.
4,390
7,250 10,780 11,710 12,520 12,800 | 13,340
0.50146 0.50226 0.50344 0.50423 0.50577 0.50693|0.51138|
L (in.)
F (lb)
L (in.) ||0.52006|0.52169|0.52362 0.52614|0.53406|0.540180.56466|
0.5
13,740 13,820 13,850 13,910| 13,990 | 14,020 | 14,130
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